Part 1)
we have that
F(x) =(x+3)²<span>−1
using a graph tool
see the attached figure N 1
we know that
t</span><span>he x-intercepts of the graph is when y=0
the points are (-4,0) and (-2,0)
</span><span>the y-intercepts of the graph is when x=0
the point is (0,8)
the graph is a vertical parabola that opens up
so
the vertex of the parabola is a minimum
the vertex is the point (-3,-1)
Part 2) </span>Write the function g(x) in the form y=a(x−h)²<span>+k . Write the equation for the line of symmetry for the graph of g(x)
</span>
we have that
G(x) =−2x²<span>+8x+3
</span><span>Group
terms that contain the same variable
</span>G(x) =(−2x²+8x)+3
Factor the
leading coefficient
G(x) =-2*(x²-4x)+3
<span>Complete
the square. Remember to balance the equation
</span>G(x) =-2*(x²-4x+4-4)+3
G(x) =-2*(x²-4x+4)+3 +8
G(x) =-2*(x²-4x+4)+11
Rewrite as perfect squares
G(x) =-2*(x-2)²+11
the answer Part 2) is
G(x) =-2*(x-2)²+11
see the attached figure N 2
the equation for the line of symmetry for the graph of g(x) is the vertical line that passes through the vertex
the vertex is the point (2,11)
so
the equation for the line of symmetry is x=2
Part 3) we have that
H (t) =−16t²<span>+28t
see the attached figure N 3
</span><span>the total length of time, in seconds, it took the dolphin to complete one jump is the difference for t=0 sec and t=1.75 sec
(1.75-0)=1.75 sec
the answer Part 3) is 1.75 sec</span>
